First you need to (require 'cl), because the Emacs "labels" macro is defined in "cl-macs.el", that is no standard part of Emacs. The main difference between "flet" and "labels" is that "labels" can be called recursively from inside a local function.

The "flet" and "labels" special operators are borrowed from Common Lisp and are ducumented in the "Common Lisp Hyperspec" under:

What I do not really understand is that first you write that you want to compute the factorial iterativeley, not recursively, but then you show Lisp code that computes the factorial recursively, but not iterativeley.

Compiling the code:

If you save the code in a file, called e.g. "binom.el", then an "Emacs-Lisp" menu appears with an entry "Byte-compile this file". If you go with the mouse pointer to "Byte-compile this file" then a "binom.elc" file will be produced from the "binom.el" file. But note that the Emacs byte compiler does not make the Lisp code run faster, the only difference is that loading the "binom.elc" file is faster than loading the "binom.el" file.

If you're looking for a Lisp with a compiler that makes the code run faster (not only loading faster), then try Common Lisp or Scheme.